That's a difficult question on almost every front. I'll try though (with a focus on Scandinavia in general, Sweden in particular since that's what I know)

What constitutes a pagan tradition?

To elaborate; for starters we have to define what that is. The introduction of Christianity did not encompass (nor require) a complete change of culture. So what parts of the culture are to be deemed 'pagan elements' and which aren't?

From a present-day point-of-view, it seems natural to distinguish statements about the natural world from those about the supernatural. The latter being a matter of faith, and therefore religion. But that distinction did not exist in the Middle Ages. To a Norseman for instance, the past or present existence of jotnar (giants) was not necessarily any less a fact than (say) the existence of a town called Paris.

Introduce Christianity and what changes here? Worshipping the Christian god is clearly at odds with worshipping the Norse ones, but it's not obvious it'd be at odds with other beliefs. On the contrary, it could even serve to confirm those beliefs. There are giants in the Bible (Nephilim). There are sea monsters like the Midgård serpent (Leviathan). Those are equivalencies that are known to have been made.

There was not necessarily any consensus on how various folk-belief figures would fit with Christianity. The Life of Paulus written by Saint Jerome around 374 contains an encounter with a figure with goat legs and horns on his head explaining he is a mortal monster, but the one worshiped by mislead believers as a satyr or faun.

That story was also repeated in the Etymologies of Saint Isidore of Seville, which was essentially the most popular encyclopedia of the Middle Ages. And it tells us that belief in satyrs, which had originally been rooted in Greek Mythology, continued. However they were now viewed as mortal creatures and were certainly not to be venerated. The Norse figures mentioned above had not been the subject of a cult in the first place.

Where do you draw the line?

There seems to be a stereotype that Medieval Christians wanted to destroy anything and everything that served as a reminder of their heathen past. So there's a lot of questions here about for instance how the weekdays were allowed to retain pagan names. And the reason is that the stereotype here isn't really true. As I point out sometimes, the Bible itself is full of mentions of pagan gods (Asherash, Chemosh, Ba'al, Molok and friends), pagan sorcery (Pharaoh's sorcerers turning sticks into snakes) and people falling into idolatry. Clearly, merely mentioning pagan deities and practices, if only as a warning example of errors and heresies, was something permitted by scripture. Hence medieval Christians did not pretend they'd never been pagan, and discussion of the old pagan ways (and the error of them) was allowed. One topic of course was the source of this error, and the typical explanation was a euhemerism. The idea that the pagan gods had been historic mortal kings of old, whose accomplishments and such had been greatly exaggerated into god-like and then god status. Thus, Jupiter and Saturn were humans who had once existed. And bearing in mind that these gods were not actual gods, one could tell the old stories about them. This is how knowledge of Greek mythology was transmitted to the future, and the same goes for Norse mythology where both the writers Snorri Sturluson and Saxo Grammaticus wrote of Odin, Thor et al as having been old Scandinavian kings. Snorri went even farther, merging his euhemerism with the older euhemerism of Greek gods and making the Norse god-kings descendants of the Greek god-kings who also were the progenitors of the Romans. (according to the Aeneid)

However, just because there's no absolute ban doesn't mean everyone was okay with (for instance) pagan names everywhere. But attitudes varied, as did the success in changing them. Take, for instance, what Saint Isidore had to say about the pagan week-day names:

Now, in a Christian mouth, the names for the days of the week sound better when they agree with the Church’s observance. If, however, it should happen that prevailing practice should draw someone into uttering with his lips what he deplores in his heart, let him understand that all those figures whose names have been given to the days of the week were themselves human. On account of certain mortal gifts they were very able and achieved distinction in this world, and so they were granted divine honors by their devotees both in the days and in the stars. But the stars were first named from the names of humans, and the days were named from the stars.

In other words, pagan day-names weren't the ideal, but when said out of old habit they could be tolerated, with the understanding these 'gods' were not gods. And the week-day names show as much as anything quite a bit of variation in how much they were altered.

Prior to Christianity being adopted either in Rome or the Germanic lands, the Germanic week-day names were calqued from the Roman ones, substituting most of the Roman god names (Mars, Mercury, Jupiter, Venus) for Germanic ones (Tyr, Odin, Thor, Freyr). After the introduction of Christianity, the Romance languages changed Saturday and Sunday to "sabbath day" and "lord's day" (e.g. sabado, domingo), but keeping most of the god names in place. In the late 10th century, (official conversion was in 1000) the Icelandic bishops managed to institute a name change and purge the pagan names from their week days (Tuesday becoming 'Third day' followed by 'Midweek day', 'Fifth day' and 'Fast day'), although the days of the sun and moon were left as-is, and so was 'wash day' which had become adopted as the Norse name for saturday. The other Scandinavian languages kept the names as they'd been. In German, Wednesday and Saturday would become 'Midweek day' and 'Sabbath day', while in English they seem to have remained what they were.

So there was not really any common standard here for whether pagan day names ought to be permitted (and if not, which ought to be changed). The force of tradition and habit is strong here as well, as seen with the many later failed attempts to change the week day names, such as the Puritans in the 17th century and the French Revolutionary Calendar in the 18th.

Anyway, so while Isidore was tolerant of pagan week day names, bishop Jón Ögmundsson of Iceland was not. But the latter also viewed dancing and music as being inherently pagan and was against those things as well. If he tried (and it seems likely he would've) he was not successful in eradicating skaldic poetry about the (ex-)gods, as Snorri recorded the Eddas a full century after Jón's death.

There are however definite limits to tolerance. Veneration of any other god beside the Christian one was absolutely not tolerated, and anything directly associated with that cult was always banned. For instance, Saint Boniface was instructed to stop the consumption of horse meat among the Germanic peoples. This was not because of a specific Christian taboo against that but because the ritual sacrifice and consumption of horses was a pagan cult practice. The Íslendingabók, describing the conversion of Iceland famously lists horsemeat consumption as being a particularly contentious issue on which the church would not budge. (but, being written 130 years after the events it purports to be described, the account cannot be read uncritically)